Abstract
Exact solutions to the self-dual Yang—Mills equations over Riemann surfaces of arbitrary genus are constructed. They are characterized by the conformal class of the Riemann surface. They correspond to U(1) instantonic solutions for an Abelian-Higgs system. A functional action of a genus g Riemann surface is constructed, with minimal points being the two-dimensional self-dual connections. The exact solutions may be interpreted as connecting initial and final nontrivial vacuum states of a conformal theory, in the sense of Segal, with a Feynman functor constructed from the functional integral of the action.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dolan, L., Phys. Rep. 109, 1.
Miura, R. M. (ed.), Bäcklund Transformations, the Inverse Scattering Method, Solutions and their Applications, Lecture Notes in Mathematics, Springer, Berlin, Heidelberg, New York, 1974. Serdaroglu, M. and Inönü E. (eds.), Proceedings of Group Theoretical Methods in Physics, Istanbul, Turkey, Lecture Notes in Physics 180, Springer, Berlin, Heidelberg, New York, 1982; Wolf, K. (ed.), Proceedings of Nonlinear Phenomenon, Oaxtefec, Mexico, Lecture Notes in Physics 189, Springer, Berlin, Heidelberg, New York, 1982; Ward, R., Integrable and solvable systems and relations among them, Preprint Univ. of Durham, 1985.
Chan, L.-L., Ge, Mo-Lin, Sinha, A. and Wu, Y. S., Phys. Lett. 121B, 391 (1983).
Hitchin, N., Proc. London Math. Soc (3) 55, 59 (1987); Lectures at LASSF 89, Caracas, Venezuela.
Martín, I., Mendoza, A., and Restuccia, A., Lett. Math. Phys. 20, 189 (1990); Rakowski, M. and Thomson, G., preprint ICTP, Trieste, IC/88/62, 1988.
Martin, I., Mendoza, A., and Restuccia, A., Lett. Math. Phys. 21, 221 (1991).
Atiyah, M. and Bott, R., Philos. Trans. Roy. Soc. London Ser. A 308, 523 (1982); Killingback, T., preprint CERN-TH 5330/89, 1989.
Segal, G., Quillen, D., Segal, G., and Tsou, S. (eds); Lecture at ‘The Interface of Mathematics and Particle Physics’ Meeting, Clarendon Press, Oxford, 1990.
Witten, E., Comm. Math. Phys. 109, 525 (1987); Killingback, T., preprint CERN-TH 5330/89, 1989; Alvarez, O., Killingback, T., Mangano, M., and Windey, T., Comm. Math. Phys. 111, 1 (1987); Witten, E., IAS preprint IASSNS-HEP-88/83, 1988.
Strominger, A., Nuclear Phys. B343 (1990); Callan, C., Harvey, J., and Strominger, A., World sheet approach to heterotic solitons and instantons, Preprint EFI-911-03, PUPT-1233, UCSB-TH-9174, 1991.
Martin, I. and Restuccia, A., Supersymmetric instantons and heterotic solitons, USB-preprint, 1991.
Naransinham, M. S. and Seshadri, C. S., Ann. of Math. 82, 540 (1965).
Belavin, A., Polyakov, A., Schwartz, A., and Tyukin, Y., Phys. Lett. 59B, 85 (1975); Witten, E., Phys. Rev. 38, 121 (1977); Jackiw, R., Nohl, C., and Rewi, C., Phys. Rev. D15, 1642 (1977).
Yang, C. N., Phys. Rev. Lett. 38, 1377 (1977).
Mandelstam, S., in M.Green and D.Gross (eds.), Unified String Theory, World Scientific, Singapore, 1986; Restuccia, A. and Taylor, J. G., Phys. Rep. 174, 285 (1989); Comm. Math. Phys. 113, 447 (1987); Aoki, K., D'Hooker, E., and Phong, D. H., preprint UCLA/89/TEP/44, 1989; Giddings, S. and Wolpert, S., Comm. Math. Phys. 109, 177 (1987); D'Hoker, E. and Giddings, S., Nuclear Phys. B291, 90 (1987).
Burnside, W., Proc. London Math. Soc. 23, 49 (1981).
Lledó, M., Martín, I., Mendoza, A., and Restuccia, A. U.S.B. preprint (1992).